Energy shifts resulting from surface curvature of quantum nanostructures

Thin layer quantization in higher dimensions and codimensions

“…Recent progress in nanotechnology caused a great activity in the field. Free particle energy spectrum was investigated for thin layers around cylinders [9], tori [10] and arbitrary surfaces of revolution [11]. In this article we clarify the general properties of the thin layer method and establish its equivalence with Prokhorov quantization procedure [12,13] for codimension 1 surfaces.…”

Curvature-induced bound states and coherent electron transport on the surface of a truncated cone

“…With the advent and development of nanostructure and quantum waveguide technology [8,9], the geometric effects were observed experimentally in some nano-devices [6,10]. For the constrained systems with novel geometries, a great deal of theoretical works have been reported [11][12][13][14][15][16]. Furthermore,in the presence of electromagnetic (EM) field with a proper choice of gauge, Giulio Ferrari and Giampaolo Cuoghi derived the surface Schrödinger equation (SSE) for a spinless charged particle constrained on a general curved surface without source current perpendicular to the thinfilm surface.…”

“…(2) is separated into normal and surface components where the first term in Eq. (7) stands for the kinetic term of the surface component [2,16,29], and…”

“…Several studies have dis-cussed the effect of the geometric potential to the electronic states [12,[19][20][21]. Geometric actions were investigated on some special surfaces of revolution [16,[22][23][24]. And the tunneling conductance of connected carbon nanotubes was studied in 1996 [25].…”

“…In this paper, we briefly review the thin-layer quantization scheme, and re-derive the SSE on the revolution surface with generatrix function, f (z), in cylindrical coordinates in Sec. II [16,26]. In Sec.…”